The idea behind the evergreen stories is that they're always fresh, i.e. forever green. For example, at a fitness magazine, which often runs stories about effective workout routines, the topic of new abdominal workouts is an evergreen one. In a fitness magazine you might see a story about abdominal workouts anytime of the year because, as an evergreen topic, it's of as much interest to readers in say, November as it is in July. Readers of a fitness magazine are always, theoretically, looking for good new abdominal workouts.
Although an evergreen story features a topic of perennial interest, these stories still need a strong hook.